CN103812587A - Group delay effect and non-linear constraint based satellite channel modeling method - Google Patents

Abstract

The invention relates to a satellite channel modeling method, particularly discloses a group delay effect and non-linear constraint based satellite channel modeling method which organically combines non-linear and group delay non-linear effects of a high-power amplifier, and solves the problem that channel models in the prior art have low simulation tracking performances of real satellite channels. A satellite channel is innovatively considered to be composed of four parts of a linear channel, a non-linear channel, a group delay channel 1 and a group delay channel 2; each part is approached by a linear part and a no-linear part of a Wiener model respectively, and when the approach process is converged, features of the Wiener model are retained; when the approach process is not converged, a control function is defined as a constraint function of input and output of the non-linear channel for replacing a non-linear function of the Wiener model so as to control convergence of the approach process. Compared with traditional satellite channel models, the group delay effect and non-linear constraint based satellite channel modeling method has the advantages of being capable of increasing a rate of convergence and reducing errors of mean square and good in dynamic tracking performance so as to guarantee satellite communication efficiency and quality.

Description

A kind of satellite channel modeling method based on group delay effect and nonlinear restriction

Technical field

The invention belongs to technical field of satellite communication, relate in particular to a kind of by the satellite channel modeling method of the non-linear of high power amplifier and the combination of group delay nonlinear effect.

Background technology

In satellite communication, communication quality is relevant with satellite channel characteristic.Whether the channel model of setting up according to satellite channel characteristic is consistent with actual channel characteristic, is the key that affects satellite communication quality.And traditional satellite channel model is considered as being formed by the linear channel model of transmitting filter, high power amplifier and the nonlinear channel Cascade of high power amplifier, as shown in Figure 1, conventional model is to carry out modeling for the non-linearity of high power amplifier, does not consider the impact of uplink communication environment in satellite communication system, emission filter and the caused group delay effect of inside satellite high power amplifier.

Conventional satellite channel model shown in Fig. 1, transmitting filter is Nyquist raised cosine filter, satellite high power amplifier is to adopt linear limit impulse response (FIR) filter and memoryless nonlinear model cascade structure.Wherein, the linear channel model of high power amplifier is expressed as with the linear segment of Wiener model

$Y\left(n\right)=\underset{i=0}{\overset{N}{\mathrm{\Σ}}}{W}_1\left(i\right)X(n-i),$

The nonlinear channel model of high power amplifier with the non-linear partial of Wiener model is

$Z\left(n\right)=\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{W}_2(n-j){\left(Y\left(n\right)\right)}^j,$

In formula, W ₁(n) the linear segment coefficient of expression Wiener model, W ₂(n) the non-linear partial coefficient of expression Wiener model, Y (n) and Z (n) are respectively the output of linear and non-linear partial; W ₁and W (n) ₂(n) adopt random gradient descent method to upgrade.In the process of approaching to reality satellite channel, there is larger error in this satellite channel Wiener model, even may occur the situation that cannot restrain.Therefore, remove the satellite channel of approaching to reality with the satellite channel Wiener model of taking no account of group delay effect, had a strong impact on satellite communication efficiency and quality.

Summary of the invention

For addressing the above problem, the invention discloses a kind of modeling method of satellite channel, the non-linear of high power amplifier and group delay nonlinear effect are organically combined, solve the prior art channel model problem low to the simulation tracing performance of real satellite channel, effectively improved satellite communication quality.

In order to achieve the above object, the invention provides following technical scheme:

A satellite channel modeling method based on group delay effect and nonlinear restriction, comprises the steps:

Steps A, system input signal a (n) obtains its output signal b (n) through linear channel; System input signal a (n) obtains its output signal b through group delay channel 1 ₁(n); System input signal a (n) obtains its output signal b through group delay channel 2 ₂(n); Wherein, n is integer, represents time series;

Step B, by the system input signal a (n) described in steps A, linear channel output signal b (n) and group delay channel 1 output signal b ₁(n), obtain nonlinear channel input signal x (n): x (n)=b (n) b through arithmetic unit 1 computing ₁(n)/a (n);

Step C, the nonlinear channel input signal x (n) described in step B, through nonlinear channel, obtains its output signal y (n);

Step D, system input signal a (n) and group delay channel 2 output signal b described in steps A ₂(n) the nonlinear channel output signal y (n) and described in step C, obtains satellite channel final output signal z (n): z (n)=y (n) b through arithmetic unit 2 computings ₂(n)/a (n);

Described linear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay linear segment; Nonlinear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay non-linear partial; Group delay channel 1 represents the nonlinear channel with group delay effect that emission filter, high power amplifier linear segment and uplink communication environment cause; Group delay channel 2 represents the nonlinear channel with group delay effect that emission filter, high power amplifier non-linear partial cause;

Wherein, linear channel output b (n) is expressed as by the linear segment of Wiener model:

$b\left(n\right)=\underset{m_0=1}{\overset{M_0}{\mathrm{\Σ}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)$

In formula, m ₀=1 ..., M ₀, M ₀for positive integer;

for linear channel C ₀(n) m ₀individual time delay tap coefficient; A (n-m ₀) be n-m ₀the signal in moment;

Described group delay channel 1, group delay channel 2 and nonlinear channel are expressed as follows by the non-linear partial of Wiener model:

Wherein, group delay channel 1 is expressed as by the non-linear partial of Wiener model:

$b_1\left(n\right)=\underset{m_1=1}{\overset{M_1}{\mathrm{\Σ}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}$

In formula, m ₁=1 ..., M ₁, M ₁for positive integer;

for group delay channel 1 weight vector C ₁(n) m ₁individual time delay tap coefficient;

Group delay channel 2 is expressed as by the non-linear partial of Wiener model:

$b_2\left(n\right)=\underset{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=1}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2}$

In formula, m ₂=1 ..., M ₂, M ₂for positive integer;

for group delay channel 2 weight vector C ₂(n) m ₂individual time delay tap coefficient;

Nonlinear channel amplitude modulation-amplitude modulation effect is expressed as by the non-linear partial of Wiener model:

$G\left(n\right)=\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3};$

In formula, ρ (n)=| x (n) | ²for the amplitude square of nonlinear channel input x (n); m ₃=1 ..., M ₃, M ₃for positive integer; G (n) represents the amplitude of nonlinear channel,

for nonlinear channel amplitude modulation-amplitude modulation effect weight vector C ₃(n) m ₃individual time delay tap coefficient;

Nonlinear channel amplitude modulation-phase modulation effect is expressed as by the non-linear partial of Wiener model:

In formula,

represent the phase place of nonlinear channel; m ₄=1 ..., M ₄, M ₄for positive integer;

for nonlinear channel amplitude modulation-phase modulation effect weight vector C ₄(n) m ₄individual tap coefficient;

Relation table between nonlinear channel input x (n)-output y (n) is shown

In formula,

for imaginary unit, lower same.

When linear channel is by the linear segment of Wiener model, when group delay channel 1, group delay channel 2 and nonlinear channel represent by the non-linear partial of Wiener model, if this model is not in the time that the process of approaching to reality satellite channel restrains, need retrain the relation of the input of group delay channel 1, group delay channel 2 and nonlinear channel and outlet chamber, constraint function is defined as:

$f\left(n\right)=\frac{1-e^{-\mathrm{\&alpha;}\left(n\right)}}{1+e^{-\mathrm{\&alpha;}\left(n\right)}}$

In formula, α (n) represents input, and f (n) represents output; To group delay channel 1, α (n) expression system input a (n), f (n) represents the output b of group delay channel 1 ₁(n); To group delay channel 2, α (n) expression system input a (n), f (n) represents the output b of group delay channel 2 ₂(n); To nonlinear channel, α (n) represents nonlinear channel input x (n), and f (n) represents nonlinear channel output y (n);

Use after constraint function, nonlinear channel input x (n) is

$x\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}{a\left(n\right)(1+e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}$

Satellite channel is always output as

$z\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}\&CenterDot;\frac{(1-e^{-\underset{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}{a\left(n\right)(1+e^{-\underset{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}$

$\&CenterDot;\left(\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3}\right)e^{j\underset{m_4=1}{\overset{M_4}{\mathrm{\&Sigma;}}}{c}_{{4m}_4}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_4}}.$

Further,

The weight vector of described linear channel more new formula is:

$C_{{0m}_0}(n+1)=C_{{0m}_0}\left(n\right)+{\mathrm{\&lambda;}}_{0}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$

The weight vector of described group delay channel 1 more new formula is:

$C_{{1m}_1}(n+1)=C_{{1m}_1}\left(n\right)+{\mathrm{\&lambda;}}_{1}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$

The weight vector of described group delay channel 2 more new formula is:

$C_{{2m}_2}(n+1)=C_{{2m}_2}\left(n\right)+{\mathrm{\&lambda;}}_{2}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$

The weight vector of described nonlinear channel amplitude modulation-amplitude modulation effect more new formula is:

$C_{{3m}_3}(n+1)=C_{{3m}_3}\left(n\right)+{\mathrm{\&lambda;}}_{3}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)},$

The weight vector of nonlinear channel amplitude modulation-phase modulation effect more new formula is:

$C_{{4m}_4}(n+1)=C_{{4m}_4}\left(n\right)+{\mathrm{\&lambda;}}_{4}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)},$

In formula, λ ₀, λ ₁, λ ₂, λ ₃, λ ₄be respectively weight vector

and

iteration step length, and 0 < λ ₀, λ ₁, λ ₂, λ ₃, λ ₄< 1; $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}$ And $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}$ Be respectively error function e (n) to weight vector

and partial derivative; ^*represent conjugation.

Compared with prior art, tool of the present invention has the following advantages and beneficial effect: the present invention is considered as satellite channel innovatively linear channel, nonlinear channel, group delay channel 1 and 2 four parts of group delay channel and forms; Each part is gone to approach by linear segment and the non-linear partial of Wiener model respectively, in the time that approximate procedure is restrained, has retained Wiener model characteristic; In the time that approximate procedure is not restrained, define the nonlinear function of a control function as the alternative Wiener model of constraint function of nonlinear channel input and output, to control approximate procedure convergence.Compared with conventional satellite channel Wiener model, the present invention has improved convergence rate, has reduced mean square error, has good performance of dynamic tracking, thereby has guaranteed efficiency and the quality of satellite communication.

Accompanying drawing explanation

Fig. 1 is satellite channel Wiener model;

Fig. 2 is the satellite channel modeling method schematic diagram based on group delay effect and nonlinear restriction provided by the invention;

Fig. 3 is nonlinear amplifier input power rollback while being 2dB, adopts respectively satellite channel Wiener model and the inventive method to approach the mean square error curve of actual channel;

Fig. 4 is nonlinear amplifier input power rollback while being 4dB, adopts respectively satellite channel Wiener model and the inventive method to approach the mean square error curve of actual channel;

Embodiment

Below with reference to specific embodiment, technical scheme provided by the invention is elaborated, should understands following embodiment and only be not used in and limit the scope of the invention for the present invention is described.

Research shows, the nonlinear effect of high power amplifier is relevant with the instantaneous power of input signal, and the signal phase nonlinear change that group delay effect causes with up link satellite communication environment, travelling-wave tube amplifier is relevant, these two kinds of effects are separate, but amplitude and the phase place of signal exert an influence, and then produce amplitude modulation-amplitude modulation and amplitude modulation-phase modulation effect.And traditional satellite channel model is to carry out modeling for the non-linearity of high power amplifier, do not consider the impact of group delay effect.In order to set up the channel model of an approaching to reality satellite channel, considering on the basis of the multiple effect of satellite channel, the present invention is considered as satellite channel to be made up of linear channel, nonlinear channel, group delay channel 1 and 2 four parts of group delay channel.

Wherein, linear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay linear segment; Nonlinear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay non-linear partial, contain amplitude modulation-amplitude modulation effect and amplitude modulation-phase modulation effect; Group delay channel 1 represents the nonlinear channel with group delay effect that emission filter, high power amplifier linear segment and uplink communication environment cause; Group delay channel 2 represents the nonlinear channel with group delay effect that emission filter, high power amplifier non-linear partial cause.On the satellite channel basis of said structure, the variation of tight tracking satellite channel characteristic of the present invention, has set up the satellite channel model with performance of dynamic tracking, and as shown in Figure 2, its step is as follows for schematic diagram:

Steps A, system input signal a (n) obtains its output signal b (n) through linear channel; System input signal a (n) obtains its output signal b through group delay channel 1 ₁(n); System input signal a (n) obtains its output signal b through group delay channel 2 ₂(n):

b(n)＝a(n)C ₀(n) (1)

b ₁(n)＝a(n)C ₁(n) (2)

b ₂(n)＝a(n)C ₂(n) (3)

Wherein, n is integer, represents time series;

Step B, by the system input signal a (n) described in steps A, linear channel output signal b (n) and group delay channel 1 output signal b ₁(n), obtain nonlinear channel input signal x (n) through arithmetic unit 1 computing:

$x\left(n\right)=\frac{b\left(n\right)b_1\left(n\right)}{a\left(n\right)}---\left(4\right)$

Step C, nonlinear channel input signal x (n) described in step B is through nonlinear channel, obtain its output signal y (n), y (n) is for x (n) is by having the nonlinear channel output of amplitude modulation-amplitude modulation and amplitude modulation-phase modulation, and contextual definition is therebetween

In formula, G (n) with

represent respectively amplitude and the phase place of nonlinear channel; for imaginary unit, lower same.

Step D, system input signal a (n) and group delay channel 2 output signal b described in steps A ₂(n) the nonlinear channel output signal y (n) and described in step C, obtains satellite channel final output signal z (n) through internalarithmetic:

$z\left(n\right)=\frac{y\left(n\right)b_2\left(n\right)}{a\left(n\right)}---\left(6\right)$

The present invention C ₀(n) weight vector of expression linear channel; Use C ₁(n) weight vector of expression group delay channel 1; Use C ₂(n) weight vector of expression group delay channel 2; Use C ₃(n) weight vector of expression nonlinear channel amplitude modulation-amplitude modulation effect; Use C ₄(n) weight vector of expression nonlinear channel amplitude modulation-phase modulation effect.

Specifically, the weight vector C of linear channel ₀(n) represented by the linear segment of Wiener model, the pass between linear channel input a (n)-output b (n) is

$b\left(n\right)=\underset{m_0=1}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)---\left(7\right)$

In formula, m ₀=1 ..., M ₀, M ₀for positive integer; c _0m(n) be linear channel C ₀(n) m ₀individual time delay tap coefficient; A (n-m ₀) be n-m ₀the signal in moment;

Group delay channel 1, group delay channel 2 and nonlinear channel are represented by the non-linear partial of Wiener model:

Group delay channel 1 is inputted a (n)-output b ₁(n) pass between is

$b_1\left(n\right)=\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}---\left(8\right)$

In formula, m ₁=1 ..., M ₁, M ₁for positive integer;

for group delay channel 1 weight vector C ₁(n) m ₁individual time delay tap coefficient; Group delay channel 2 is inputted a (n)-output b ₂(n) pass between is

$b_2\left(n\right)=\underset{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=1}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{m_2}---\left(9\right)$

In formula, m ₂=1 ..., M ₂, M ₂for positive integer; c _2m(n) be group delay channel 2 weight vector C ₂(n) m ₂individual time delay tap coefficient; Nonlinear channel amplitude modulation-amplitude modulation effect is expressed as by the non-linear partial of Wiener model

$G\left(n\right)=\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3}---\left(10\right)$

In formula, ρ (n)=| x (n) | ²for the amplitude square of x (n); m ₃=1 ..., M ₃, M ₃for positive integer; G (n) represents the amplitude of nonlinear channel,

for nonlinear channel amplitude modulation-amplitude modulation effect weight vector C ₃(n) m ₃individual time delay tap coefficient; Nonlinear channel amplitude modulation-phase modulation effect is expressed as by the non-linear partial of Wiener model

In formula, G (n) represents the phase place of nonlinear channel; m ₄=1 ..., M ₄, M ₄for positive integer;

for nonlinear channel amplitude modulation-phase modulation effect weight vector C ₄(n) m ₄individual time delay tap coefficient.At this moment, the relation table between nonlinear channel input x (n)-output y (n) is shown

When linear channel is by the linear segment of Wiener model, when group delay channel 1, group delay channel 2 and nonlinear channel represent by the non-linear partial of Wiener model, if this model is not in the time that the process of approaching to reality satellite channel restrains, need retrain the relation of the input of group delay channel 1, group delay channel 2 and nonlinear channel and outlet chamber, constraint function is defined as:

$f\left(n\right)=\frac{1-e^{-\mathrm{\&alpha;}\left(n\right)}}{1+e^{-\mathrm{\&alpha;}\left(n\right)}}---\left(13\right)$

In formula, α (n) represents input, and f (n) represents output.

To group delay channel 1, α (n) expression system input a (n), f (n) represents the output b of group delay channel 1 ₁(n), to group delay channel 2, α (n) expression system input a (n), f (n) represents the output b of group delay channel 2 ₂(n), to nonlinear channel, α (n) represents nonlinear channel input x (n), and f (n) represents nonlinear channel output y (n), uses after constraint function, and nonlinear channel input x (n) is

$x\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}{a\left(n\right)(1+e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}---\left(14\right)$

$z\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}\&CenterDot;\frac{(1-e^{-\underset{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}{a\left(n\right)(1+e^{-\underset{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="140212111634.png"\; state="\{\{state\}\}">m</figure-callout>}}_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}$

$\&CenterDot;\left(\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3}\right)e^{j\underset{m_4=1}{\overset{M_4}{\mathrm{\&Sigma;}}}{c}_{{4m}_4}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_4}}---\left(15\right)$

By Fig. 2, error function is defined as

In e (n)=z (n)-d (n) (16) formula, d (n) is the output of real satellite channel.

The cost function of approximate procedure is defined as

J(n)＝E{|e(n)| ²} (17)

In formula, E represents mathematic expectaion.When the cost function of approximate procedure is got when minimum, by the descent method of degree of passing at random of cost function, the weight vector that obtains linear channel, group delay channel and nonlinear channel more new formula is

$C_{{0m}_0}(n+1)=C_{{0m}_0}\left(n\right)+{\mathrm{\&lambda;}}_{0}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)}---\left(18\right)$

$C_{{1m}_1}(n+1)=C_{{1m}_1}\left(n\right)+{\mathrm{\&lambda;}}_{1}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)}---\left(19\right)$

$C_{{2m}_2}(n+1)=C_{{2m}_2}\left(n\right)+{\mathrm{\&lambda;}}_{2}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)}---\left(20\right)$

$C_{{3m}_3}(n+1)=C_{{3m}_3}\left(n\right)+{\mathrm{\&lambda;}}_{3}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}---\left(21\right)$

$C_{{4m}_4}(n+1)=C_{{4m}_4}\left(n\right)+{\mathrm{\&lambda;}}_{4}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}---\left(22\right)$

In formula, λ ₀, λ ₁, λ ₂, λ ₃, λ ₄be respectively weight vector

and

iteration step length, and 0 < λ ₀, λ ₁, λ ₂, λ ₃, λ ₄< 1; $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}$ And $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}$ Be respectively error function e (n) to weight vector

and

partial derivative; ^*represent conjugation.

Embodiment:

We compare method provided by the invention and conventional satellite channel Wiener model, further to verify validity of the present invention.

It is 8PSK signal that experiment adopts transmitting modulation signal, and transmitting filter is that roll-off factor is 0.5, each symbol is the square root raised cosine filter of 8 sampling points, and weight vector adopts center initialization method; Wiener model neutral line channel and nonlinear channel weight vector iteration step length are 0.0008; In the inventive method, the weight vector of linear channel, nonlinear channel, group delay channel is counted iteration step length and is 0.0005.

Fig. 3 and Fig. 4 are respectively nonlinear amplifier input power rollback while being 2dB and 4dB, and two kinds of methods are approached the mean square error curve of actual channel.Input power rollback is input signal power while representing that amplifier is operated in saturation point and the difference of real input signal power, and its value is less, and non-linear amplitude modulation-amplitude modulation and amplitude modulation-phase modulation effect are stronger, cause that the nonlinear distortion of signal is more serious.

Can find out by Fig. 3 and Fig. 4, at initial period, the mean square error of the inventive method institute established model output is just little than conventional satellite channel Wiener model.For example, while being 2dB and iteration 1000 times for input power rollback, the mean square error of the inventive method institute established model output is just than the approximately little 10dB of conventional satellite channel Wiener model, and the convergence rate of the inventive method institute established model is than fast approximately 3500 steps of conventional satellite channel Wiener model; While being 4dB and iteration 1000 times for input power rollback, the mean square error of the inventive method institute established model output is just than the approximately little 12dB of conventional satellite channel Wiener model, and the convergence rate of the inventive method institute established model is than fast approximately 4000 steps of conventional satellite channel Wiener model.Therefore,, compared with conventional satellite channel Wiener model, the inventive method fast convergence rate, mean square error are little, have good performance of dynamic tracking.

The disclosed technological means of the present invention program is not limited only to the disclosed technological means of above-mentioned execution mode, also comprises the technical scheme being made up of above technical characterictic combination in any.It should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.

Claims (2)

1. the satellite channel modeling method based on group delay effect and nonlinear restriction, is characterized in that, comprises the steps:

Steps A, system input signal a (n) obtains its output signal b (n) through linear channel; System input signal a (n) obtains its output signal b through group delay channel 1 ₁(n); System input signal a (n) obtains its output signal b through group delay channel 2 ₂(n); Wherein, n is integer, represents time series;

Step B, by the system input signal a (n) described in steps A, linear channel output signal b (n) and group delay channel 1 output signal b ₁(n), obtain nonlinear channel input signal x (n): x (n)=b (n) b through arithmetic unit 1 computing ₁(n)/a (n);

Step C, the nonlinear channel input signal x (n) described in step B, through nonlinear channel, obtains its output signal y (n);

Step D, system input signal a (n) and group delay channel 2 output signal b described in steps A ₂(n) the nonlinear channel output signal y (n) and described in step C, obtains satellite channel final output signal z (n): z (n)=y (n) b through arithmetic unit 2 computings ₂(n)/a (n);

Described linear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay linear segment; Nonlinear channel by emission filter, uplink communication environment and inside satellite high power amplifier without the cascade of group delay non-linear partial; Group delay channel 1 represents the nonlinear channel with group delay effect that emission filter, high power amplifier linear segment and uplink communication environment cause; Group delay channel 2 represents the nonlinear channel with group delay effect that emission filter, high power amplifier non-linear partial cause;

Described linear channel is expressed as by the linear segment of Wiener model:

$b\left(n\right)=\underset{m_0=1}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0),$

In formula, m ₀=1 ..., M ₀, M ₀for positive integer;

for linear channel C ₀(n) m ₀individual time delay tap coefficient; Described group delay channel 1, group delay channel 2 and nonlinear channel are expressed as follows by the non-linear partial of Wiener model: wherein, group delay channel 1 is expressed as by the non-linear partial of Wiener model:

$b_1\left(n\right)=\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1},$

In formula, m ₁=1 ..., M ₁, M ₁for positive integer;

for group delay channel 1 weight vector C ₁(n) _m1 time delay tap coefficient;

Group delay channel 2 is expressed as by the non-linear partial of Wiener model:

$b_2\left(n\right)=\underset{m_2=1}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{m_2},$

In formula, m ₂=1 ..., M ₂, M ₂for positive integer; c _2m(n) be group delay channel 2 weight vector C ₂(n) m ₂individual time delay tap coefficient;

Nonlinear channel amplitude modulation-amplitude modulation effect is expressed as by the non-linear partial of Wiener model:

$G\left(n\right)=\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3},$

In formula, ρ (n)=| x (n) | ²for the amplitude square of nonlinear channel input x (n); m ₃=1 ..., M ₃, M ₃for positive integer; G (n) represents the amplitude of nonlinear channel, for nonlinear channel amplitude modulation-amplitude modulation effect weight vector C ₃(n) m ₃individual time delay tap coefficient;

Nonlinear channel amplitude modulation-phase modulation effect is expressed as by the non-linear partial of Wiener model:

In formula, represent the phase place of nonlinear channel; m ₄=1 ..., M ₄, M ₄for positive integer; for nonlinear channel amplitude modulation-phase modulation effect weight vector C ₄(n) m ₄individual time delay tap coefficient;

Relation table between nonlinear channel input x (n)-output y (n) is shown

In formula,

for imaginary unit, lower same;

When linear channel is by the linear segment of Wiener model, when group delay channel 1, group delay channel 2 and nonlinear channel represent by the non-linear partial of Wiener model, if this model is not in the time that the process of approaching to reality satellite channel restrains, need retrain the relation of the input of group delay channel 1, group delay channel 2 and nonlinear channel and outlet chamber, constraint function is defined as:

$f\left(n\right)=\frac{1-e^{-\mathrm{\&alpha;}\left(n\right)}}{1+e^{-\mathrm{\&alpha;}\left(n\right)}},$

In formula, α (n) represents input, and f (n) represents output; To group delay channel 1, α (n) expression system input a (n), f (n) represents the output b of group delay channel 1 ₁(n); To group delay channel 2, α (n) expression system input a (n), f (n) represents the output b of group delay channel 2 ₂(n); To nonlinear channel, α (n) represents nonlinear channel input x (n), and f (n) represents nonlinear channel output y (n);

Use after constraint function, nonlinear channel input x (n) is

$x\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})}{a\left(n\right)(1+e^{-\underset{m_1=1}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{m_1}})},$

Satellite channel is always output as

$z\left(n\right)=\frac{\underset{m_0=0}{\overset{M_0}{\mathrm{\&Sigma;}}}{c}_{{0m}_0}\left(n\right)a(n-m_0)(1-e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}{a\left(n\right)(1+e^{-\underset{m_1=0}{\overset{M_1}{\mathrm{\&Sigma;}}}{c}_{{1m}_1}\left(n\right){\left(a\left(n\right)\right)}^{M_1}})}\&CenterDot;\frac{(1-e^{-\underset{m_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}{a\left(n\right)(1+e^{-\underset{m_2=0}{\overset{M_2}{\mathrm{\&Sigma;}}}{c}_{{2m}_2}\left(n\right){\left(a\left(n\right)\right)}^{M_2}})}$

$\&CenterDot;\left(\underset{m_3=1}{\overset{M_3}{\mathrm{\&Sigma;}}}{c}_{{3m}_3}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_3}\right)e^{j\underset{m_4=1}{\overset{M_4}{\mathrm{\&Sigma;}}}{c}_{{4m}_4}\left(n\right){\left(\mathrm{\&rho;}\left(n\right)\right)}^{M_4}}.$

2. the satellite channel modeling method based on group delay effect and nonlinear restriction according to claim 1, is characterized in that: the weight vector of described linear channel more new formula is:

$C_{{0m}_0}(n+1)=C_{{0m}_0}\left(n\right)+{\mathrm{\&lambda;}}_{0}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$

The weight vector of described group delay channel 1 more new formula is:

$C_{{1m}_1}(n+1)=C_{{1m}_1}\left(n\right)+{\mathrm{\&lambda;}}_{1}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$

The weight vector of described group delay channel 2 more new formula is:

$C_{{2m}_2}(n+1)=C_{{2m}_2}\left(n\right)+{\mathrm{\&lambda;}}_{2}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$

The weight vector of described nonlinear channel amplitude modulation-amplitude modulation effect more new formula is:

$C_{{3m}_3}(n+1)=C_{{3m}_3}\left(n\right)+{\mathrm{\&lambda;}}_{3}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)},$

The weight vector of nonlinear channel amplitude modulation-phase modulation effect more new formula is:

$C_{{4m}_4}(n+1)=C_{{4m}_4}\left(n\right)+{\mathrm{\&lambda;}}_{4}e\left(n\right)\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)},$

In formula, λ ₀, λ ₁, λ ₂, λ ₃, λ ₄be respectively weight vector

and

iteration step length, and 0 < λ ₀, λ ₁, λ ₂, λ ₃, λ ₄< 1; $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{0m_0}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{1m_1}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{2m_2}\left(n\right)},$ $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{3m_3}\left(n\right)}$ And $\frac{{\&PartialD;e}^{*}\left(n\right)}{{\&PartialD;C}_{4m_4}\left(n\right)}$ Be respectively error function e (n) to weight vector and partial derivative; ^*represent conjugation.

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